Sim-Heuristic Approach for Solving Discrete Optimization Problems with Stochastic Constraints

Discrete optimization problems with stochastic constraints (DOPSC) are discrete optimization problems that involve constraints defined by stochastic processes. Solving DOPSC is highly time-consuming, as the number of combinations grows exponentially with problem size. The ordinal optimization (OO) framework provides a feasible alternative for solving DOPSC. Nonetheless, stochastic constraints affect the efficiency of the OO framework. In this research, a sim-heuristic approach integrating manta ray foraging optimization with ordinal optimization (MRFOO) is developed to solve DOPSC reasonably. The MRFOO consists of three fundamental processes: model simulator, explorative search, and exploitative search. First, a model simulator is developed to assess the performance of a decision vector. Secondly, the reformed manta ray foraging optimization is employed to choose N superior decision vectors from the search space. Then, the modified optimal computing budget allocation is applied to decide a prominent decision vector from N superior decision vectors. Finally, the MRFOO is applied to determine the optimal number of agents in multi-skill call centers for minimizing total costs while meeting service level requirements. The applicability of the MRFOO is verified by two numerical examples and compared with four heuristic approaches. Experimental results show that the MRFOO converges more effectively to near optimum during the search process.